2 citations · 4 across the 18 of their papers we have counts for
21 papers
Randomized Zero Forcing
Jesse Geneson, Illya Hicks, Noah Lichtenberg +2
We introduce randomized zero forcing (RZF), a stochastic color-change process on directed graphs in which a white vertex turns blue with probability equal to the fraction of its in…
Characterizing QUBO Reformulations of the Max-k-Cut Problem for Quantum Computing
Adrian Harkness, Hamidreza Validi, Ramin Fakhimi +4
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this…
Optimizing Cost Hamiltonian Compilation for Max-Cut QAOA on Unweighted Graphs Using Global Controls and Qubit Bit Flips
Saber Dinpazhouh, Illya V. Hicks
We study a cost Hamiltonian compilation problem for the quantum approximate optimization algorithm (QAOA) applied to the Max-Cut problem, focusing on trapped-ion quantum computers.…
Optimal Mixed Integer Linear Optimization Trained Multivariate Classification Trees
Brandon Alston, Illya V. Hicks
Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree h…
Combinatorial Disjunctive Constraints for Obstacle Avoidance in Path Planning
Raul Garcia, Illya V. Hicks, Joey Huchette
We present a new approach for modeling avoidance constraints in 2D environments, in which waypoints are assigned to obstacle-free polyhedral regions. Constraints of this form are o…
On relaxations of the max -cut problem formulations
Ramin Fakhimi, Hamidreza Validi, Illya V. Hicks +2
A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max -cut problem is a…
Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions
Bochuan Lyu, Illya V. Hicks, Joey Huchette
We study mixed-integer programming formulations for the piecewise linear lower and upper bounds (in other words, piecewise linear relaxations) of nonlinear functions that can be mo…
Maximal Clique and Edge-Ranking Bounds of Biclique Cover Number
Bochuan Lyu, Illya V. Hicks
The biclique cover number of a graph denotes the minimum number of complete bipartite (biclique) subgraphs to cover all the edges of the graph. In this paper, we…
Mixed integer linear optimization formulations for learning optimal binary classification trees
Brandon Alston, Hamidreza Validi, Illya V. Hicks
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision tree…
Modeling Combinatorial Disjunctive Constraints via Junction Trees
Bochuan Lyu, Illya V. Hicks, Joey Huchette
We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We p…
Finding Biclique Partitions of Co-Chordal Graphs
Bochuan Lyu, Illya V. Hicks
The biclique partition number of a graph is referred to as the least number of complete bipartite (biclique) subgraphs that are required to cover the edges of the…
Optimal Sensor Placement in Power Grids: Power Domination, Set Covering, and the Neighborhoods of Zero Forcing Forts
Logan A. Smith, Illya V. Hicks
To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable…
An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs
Logan A. Smith, David T. Mildebrath, Illya V. Hicks
We present an integer programming model to compute the strong rainbow connection number, , of any simple graph . We introduce several enhancements to the proposed model,…
A Polynomial Time Algorithm for Computing the Strong Rainbow Connection Numbers of Odd Cacti
Logan A. Smith, David T. Mildebrath, Illya V. Hicks
We consider the problem of computing the strong rainbow connection number for cactus graphs in which all cycles have odd length. We present a formula to calculate $src…
Power domination throttling
Boris Brimkov, Joshua Carlson, Illya V. Hicks +2
A power dominating set of a graph is a set that colors every vertex of according to the following rules: in the first timestep, every vertex in be…
Computational Approaches for Zero Forcing and Related Problems
Boris Brimkov, Caleb C. Fast, Illya V. Hicks
In this paper, we propose computational approaches for the zero forcing problem, the connected zero forcing problem, and the problem of forcing a graph within a specified number of…
Graphs with Extremal Connected Forcing Numbers
Boris Brimkov, Caleb C. Fast, Illya V. Hicks
Zero forcing is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The…
Complexity and Computation of Connected Zero Forcing
Boris Brimkov
Zero forcing is an iterative graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. It is NP-hard to find a minimum ze…
Chromatic and flow polynomials of generalized vertex join graphs and outerplanar graphs
Boris Brimkov, Illya V. Hicks
A generalized vertex join of a graph is obtained by joining an arbitrary multiset of its vertices to a new vertex. We present a low-order polynomial time algorithm for finding the…
A Note on Integer Domination of Cartesian Product Graphs
K. Choudhary, S. Margulies, I. V. Hicks
Given a graph , a dominating set is a set of vertices such that any vertex in has at least one neighbor (or possibly itself) in . A -dominating multiset is…
A Note on Total and Paired Domination of Cartesian Product Graphs
K. Choudhary, S. Margulies, I. V. Hicks
A dominating set for a graph is a subset of such that any vertex not in has at least one neighbor in . The domination number is the size of a minimum d…